The ratio of escape velocity at earth (υ_e) to the escape velocity at a planet (υ_p) whose radius and mean density are twice as that of earth is : 

1 : 2\(\sqrt{2}\)

\(v_e = \sqrt{\frac{2GM}{R}} \)

M = \(\frac{4}{3} \pi R^3 \rho\)

⇒ \(v_e = \sqrt{\frac{8 \pi G \rho R^2}{3}} \)

⇒ \(v_p = \sqrt{\frac{8 \pi G (2\rho) (2R)^2}{3}} \)

⇒ v_p = 2\(\sqrt{2}\) v_e

∴ \(\frac{v_e}{v_p}\) = \(\frac{1}{2\sqrt{2}}\)